We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-4,
author = {A. Raouf Chouikha},
title = {Monotonicity of the period function for some planar differential systems. Part II: Li\'enard and related systems},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {405-424},
zbl = {1161.34021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-4}
}
A. Raouf Chouikha. Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems. Applicationes Mathematicae, Tome 32 (2005) pp. 405-424. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-4/